Answer
(a) The unit matrix $I_3$, that is
$$I_3=\left[\begin{array}{ll}{1} & {0} &{0}\\ {0} & {1}&{0}\\{0}&{0}&{1}\end{array}\right].$$
(b) The matrices on the form
$$\left[\begin{array}{ll}{1} & {0} &{a}\\ {0} & {1}&{b}\\{0}&{0}&{0}\end{array}\right], \quad a,b\in R.$$
For example, the matrix $$\left[\begin{array}{ll}{1} & {0} &{3}\\ {0} & {1}&{-2}\\{0}&{0}&{0}\end{array}\right].$$
(c) The matrices on the form $$\left[\begin{array}{ll}{1} & {a} &{b}\\ {0} & {0}&{0}\\{0}&{0}&{0}\end{array}\right],\quad a,b\in R$$
For example, the matrix $$\left[\begin{array}{ll}{1} & {-6} &{-5}\\ {0} & {0}&{0}\\{0}&{0}&{0}\end{array}\right].$$
Work Step by Step
The possible $3\times 3$ reduced row-echelon matrices can be one of the following forms:
(a) The unit matrix $I_3$, that is
$$I_3=\left[\begin{array}{ll}{1} & {0} &{0}\\ {0} & {1}&{0}\\{0}&{0}&{1}\end{array}\right].$$
(b) The matrices on the form
$$\left[\begin{array}{ll}{1} & {0} &{a}\\ {0} & {1}&{b}\\{0}&{0}&{0}\end{array}\right], \quad a,b\in R.$$
For example, the matrix $$\left[\begin{array}{ll}{1} & {0} &{3}\\ {0} & {1}&{-2}\\{0}&{0}&{0}\end{array}\right].$$
(c) The matrices on the form $$\left[\begin{array}{ll}{1} & {a} &{b}\\ {0} & {0}&{0}\\{0}&{0}&{0}\end{array}\right],\quad a,b\in R$$
For example, the matrix $$\left[\begin{array}{ll}{1} & {-6} &{-5}\\ {0} & {0}&{0}\\{0}&{0}&{0}\end{array}\right].$$
